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Math Help - 3 Probablity problems.. multiplication rule

  1. #1
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    Unhappy 3 Probablity problems.. multiplication rule

    If anyone can solve them for me I'd be really thankful. I have to take an exam soon and I can't get past these stupid 3 problems! It's driving me crazy. An answer has to be rounded 3 decimal points. Example: .038
    These problems have to do with the multiplication rule and such.

    1. License plates in my city consists of 3 letters followed by 3 integers. Repeats are allowed. If I select a license plate at random, find the probability that it has the letter J on it.

    2. I will randomly rearrange the first 11 letters of the alphabet. Find the probability that the rearrangement has no vowel in the first five places.

    3. I roll a fair die 4 times. Find the probablity that I see a "2" or "3" on both the first and last roll.


    If anyone can solve these, you are a god.
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  2. #2
    Moo
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    Hello,

    I'll try to do it... However, you will have to check by yourself if it seems correct, because I still haven't found any way to check this kind of exercises

    Quote Originally Posted by ohsosketro View Post
    1. License plates in my city consists of 3 letters followed by 3 integers. Repeats are allowed. If I select a license plate at random, find the probability that it has the letter J on it.
    Let \Omega be the set of all possible plates.
    Let A be the set of "plates containing letter J on it".
    Since there is equiprobability to find a plate comparing to another :

    P(A)=\frac{|A|}{|\Omega|}

    For 1 letter, there are 26 possibilities.
    For 1 integer, there are 10 possibilities (0 to 9).
    Since repeats are allowed, there are 26^3 \cdot 10^3 possible plates. This is |\Omega|

    Now, 1 letter is fixed to J.
    So we will have to choose for 2 letters and 3 integers. Once again, repeats are allowed. Therefore, there are 26^2 \cdot 10^3 possible plates. This is |A|

    ---> \boxed{P(A)=\frac{1}{26}}

    I know there is a shorter way, but I've been taught that we can avoid more easily mistakes by doing this way...
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  3. #3
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    Thanks the answer ended up being .111
    I really hate this type of math. lol
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  4. #4
    Moo
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    Quote Originally Posted by ohsosketro View Post
    Thanks the answer ended up being .111
    I really hate this type of math. lol
    Ok what's wrong then ? 1/26 ~ 0.038

    I hate it too ~
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  5. #5
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    I hate it also because every time I get the problems wrong I get a new set of 3 problems. Even if I get 2/3 I have to do 3 new ones..
    I have 3 news ones that are

    1. Lisence plates in my city consist of 2 letters followed by 4 integers. Repeats are allowed. If I select a plate at random, Find the probability that it has no repeated letters or integers.

    2. I will rearrange the first 11 letters of the alphabet. Find the probability that the arrangement starts and ends with a vowel.

    3. I roll a fair die 6 times. Find the probablity that I see a "6" on both the first and last roll.


    I'm never gonna get them right.
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